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arXiv:quant-ph/0608068 · Physical Review A

Physical implementation of holonomic quantum computation in decoherence-free subspaces with trapped ions

Xin Ding Zhang, Qinghua Zhang, Z. D. Wang

Published Sep 13, 2006• 45 citations
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Abstract

We propose a feasible scheme to achieve holonomic quantum computation in a decoherence-free subspace (DFS) with trapped ions. By the application of appropriate bichromatic laser fields on the designated ions, we are able to construct two noncommutable single-qubit gates and one controlled-phase gate using the holonomic scenario in the encoded DFS.

DOI
10.1103/physreva.74.034302

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We propose a feasible scheme to achieve holonomic quantum computation in a decoherence-free subspace (DFS) with trapped ions. By the application of appropriate bichromatic laser fields on the designated ions, we are able to construct two noncommutable single-qubit gates and one controlled-phase gate using the holonomic scenario in the encoded DFS.
Implementing nonadiabatic holonomic quantum computation in decoherence-free subspaces may consolidate the advantages of both strategies and thus leads to suppression of both local and collective noises. In a recent paper, Xu et al. [Phys. Rev. Lett. 109, 170501 (2012)] proposed an interesting implementation of such a scheme; however, four-body interaction, which is hard to achieve in a realistic system, is required there. In this paper we propose a simplified scheme to implement such single-qubit and two-qubit logical operations by utilizing only two-body interactions, which is much easier to realize in a trapped ion system.
Nonadiabatic holonomic quantum computation in decoherence-free subspaces has attracted increasing attention recently, as it allows for high-speed implementation and combines both the robustness of holonomic gates and the coherence stabilization of decoherence-free subspaces. Since the first protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces, a number of schemes for its physical implementation have been put forward. However, all previous schemes require two noncommuting gates to realize an arbitrary one-qubit gate, which doubles the exposure time of gates to error sources as well as the resource expenditure. In this paper, we propose an alternative protocol for nonadiabatic holonomic quantum computation in decoherence-free subspaces, in which an arbitrary one-qubit gate in decoherence-free subspaces is realized by a single-shot implementation. The present protocol not only maintains the merits of the original protocol but also avoids the extra work of combining two gates to implement an arbitrary one-qubit gate and thereby reduces the exposure time to various error sources.
Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, nonadiabatic holonomic quantum computation in decoherence-free subspaces, which avoids a long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize nonadiabatic holonomic quantum computation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.
We propose a decoherence-free subspace (DFS) scheme to realize scalable quantum computation with trapped ions. The spin-dependent laser-ion coupling is exploited in the presence of Coulomb interactions. A universal set of unconventional geometric quantum gates is achieved in encoded subspaces that are immune from decoherence by collective dephasing. The scalability of the scheme for an ion-array system is demonstrated, either by adiabatically switching on and off the interactions, or by a fast gate scheme with DFS encoding and noise-decoupling techniques.
Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of (N - 2)/N. The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.